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Cardinality of Sets

If 2Q+3P=3P...

Question

If $2 Q + 3 P = \frac{3 P - Q}{2 R}$ , express P in terms of Q and R. Find the value of P, when $R = - 2$ and $Q = 1$ .

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Solution

Given, $2 Q + 3 P = \frac{3 P - Q}{2 R}$
$=> 4 R Q + 6 P R = 3 P - Q$
$=> 6 P R - 3 P = - 4 R Q - Q$
$=> 3 P (2 R - 1) = - Q (4 R + 1)$
$=> 3 P (1 - 2 R) = Q (4 R + 1)$
$=> P = \frac{Q (4 R + 1)}{3 (1 - 2 R)}$
When, $R = - 2, Q = 1$ , we have
$=> P = \frac{1 (4 \times (- 2) + 1)}{3 (1 - 2 \times (- 2))}$
$=> P = \frac{- 7}{15}$

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